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<li><a class="reference internal" href="#">Hierarchical clustering: structured vs unstructured ward</a></li>
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<div class="sphx-glr-example-title section" id="hierarchical-clustering-structured-vs-unstructured-ward">
<span id="sphx-glr-auto-examples-cluster-plot-ward-structured-vs-unstructured-py"></span><h1>Hierarchical clustering: structured vs unstructured ward<a class="headerlink" href="#hierarchical-clustering-structured-vs-unstructured-ward" title="Permalink to this headline">¶</a></h1>
<p>Example builds a swiss roll dataset and runs
hierarchical clustering on their position.</p>
<p>For more information, see <a class="reference internal" href="../../modules/clustering.html#hierarchical-clustering"><span class="std std-ref">Hierarchical clustering</span></a>.</p>
<p>In a first step, the hierarchical clustering is performed without connectivity
constraints on the structure and is solely based on distance, whereas in
a second step the clustering is restricted to the k-Nearest Neighbors
graph: it’s a hierarchical clustering with structure prior.</p>
<p>Some of the clusters learned without connectivity constraints do not
respect the structure of the swiss roll and extend across different folds of
the manifolds. On the opposite, when opposing connectivity constraints,
the clusters form a nice parcellation of the swiss roll.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Authors : Vincent Michel, 2010</span>
<span class="c1">#           Alexandre Gramfort, 2010</span>
<span class="c1">#           Gael Varoquaux, 2010</span>
<span class="c1"># License: BSD 3 clause</span>

<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>

<span class="kn">import</span> <span class="nn">time</span> <span class="k">as</span> <span class="nn">time</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">mpl_toolkits.mplot3d.axes3d</span> <span class="k">as</span> <span class="nn">p3</span>
<span class="kn">from</span> <span class="nn">sklearn.cluster</span> <span class="kn">import</span> <span class="n">AgglomerativeClustering</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_swiss_roll</span>

<span class="c1"># #############################################################################</span>
<span class="c1"># Generate data (swiss roll dataset)</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">1500</span>
<span class="n">noise</span> <span class="o">=</span> <span class="mf">0.05</span>
<span class="n">X</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">make_swiss_roll</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">noise</span><span class="p">)</span>
<span class="c1"># Make it thinner</span>
<span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">*=</span> <span class="o">.</span><span class="mi">5</span>

<span class="c1"># #############################################################################</span>
<span class="c1"># Compute clustering</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Compute unstructured hierarchical clustering...&quot;</span><span class="p">)</span>
<span class="n">st</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">ward</span> <span class="o">=</span> <span class="n">AgglomerativeClustering</span><span class="p">(</span><span class="n">n_clusters</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span> <span class="n">linkage</span><span class="o">=</span><span class="s1">&#39;ward&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">elapsed_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">st</span>
<span class="n">label</span> <span class="o">=</span> <span class="n">ward</span><span class="o">.</span><span class="n">labels_</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Elapsed time: </span><span class="si">%.2f</span><span class="s2">s&quot;</span> <span class="o">%</span> <span class="n">elapsed_time</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Number of points: </span><span class="si">%i</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">label</span><span class="o">.</span><span class="n">size</span><span class="p">)</span>

<span class="c1"># #############################################################################</span>
<span class="c1"># Plot result</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">p3</span><span class="o">.</span><span class="n">Axes3D</span><span class="p">(</span><span class="n">fig</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">view_init</span><span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="o">-</span><span class="mi">80</span><span class="p">)</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">label</span><span class="p">):</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">label</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">label</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">label</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span>
               <span class="n">color</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">jet</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">label</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)),</span>
               <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Without connectivity constraints (time </span><span class="si">%.2f</span><span class="s1">s)&#39;</span> <span class="o">%</span> <span class="n">elapsed_time</span><span class="p">)</span>


<span class="c1"># #############################################################################</span>
<span class="c1"># Define the structure A of the data. Here a 10 nearest neighbors</span>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <span class="n">kneighbors_graph</span>
<span class="n">connectivity</span> <span class="o">=</span> <span class="n">kneighbors_graph</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">n_neighbors</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">include_self</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>

<span class="c1"># #############################################################################</span>
<span class="c1"># Compute clustering</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Compute structured hierarchical clustering...&quot;</span><span class="p">)</span>
<span class="n">st</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">ward</span> <span class="o">=</span> <span class="n">AgglomerativeClustering</span><span class="p">(</span><span class="n">n_clusters</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span> <span class="n">connectivity</span><span class="o">=</span><span class="n">connectivity</span><span class="p">,</span>
                               <span class="n">linkage</span><span class="o">=</span><span class="s1">&#39;ward&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">elapsed_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">st</span>
<span class="n">label</span> <span class="o">=</span> <span class="n">ward</span><span class="o">.</span><span class="n">labels_</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Elapsed time: </span><span class="si">%.2f</span><span class="s2">s&quot;</span> <span class="o">%</span> <span class="n">elapsed_time</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Number of points: </span><span class="si">%i</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">label</span><span class="o">.</span><span class="n">size</span><span class="p">)</span>

<span class="c1"># #############################################################################</span>
<span class="c1"># Plot result</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">p3</span><span class="o">.</span><span class="n">Axes3D</span><span class="p">(</span><span class="n">fig</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">view_init</span><span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="o">-</span><span class="mi">80</span><span class="p">)</span>
<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">label</span><span class="p">):</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">label</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">label</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">label</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span>
               <span class="n">color</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">jet</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">label</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)),</span>
               <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;With connectivity constraints (time </span><span class="si">%.2f</span><span class="s1">s)&#39;</span> <span class="o">%</span> <span class="n">elapsed_time</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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